Question

A woman went shopping. First she spent 4/5 of all money she had in her purse, and then she lost 2/3 of what was remaining. Now she has $10 left.

How much money did she lose

Answer 1

The woman initially had $50 and lost approximately $33.33.

Step-by-step explanation:

To determine the amount of money the woman lost, we need to work backwards from the $10 she has left. Let's start by finding out how much money she had before losing any. We know that after spending 4/5 of her money, she has 1/5 remaining. And we also know that this 1/5 is equal to $10. So, we can set up the equation: 1/5 * x = $10, where x represents the total amount of money she had. To solve for x, we can multiply both sides of the equation by 5 to isolate the x. This gives us: x = $10 * 5 = $50. Therefore, the woman had $50 before losing any.

Next, we need to find out how much money she lost after losing 2/3 of what was remaining. We can calculate this by multiplying the remaining amount by 2/3. In this case, the remaining amount is $50. So, she lost: 2/3 * $50 = $33.33. Therefore, the woman lost approximately $33.33.

Answer 2

She lost $20

Step-by-step explanation:

This is a 2 step problem

Let's call x the total amount of money in her purse.

First, the woman spent 4/5 of her money --> 4/5x

Then, she spent 2/3 of the remainder --> (2/3)(4/5x)

Let's take the difference of her total and what she spent.

10 = x - ((4/5x) + ((2/3)(1/5x))) --> combine like terms

10 = x - ((12/15x) + (2/15x))

10 = x - (14/15x)

10 = 1/15x

x = 10*15

x = 150

If she lost 2/15x

(2/15)(150) = 20